Authors: Yi Cao
In SunQM-4, to build a full-QM deduced Solar system’s 3D probability density map with time-dependent orbital movement, we developed a non-Born probability (NBP) method. In the current paper, we showed that NBP is directly proportional to the wave function (rather than Born probability’s conjugated-squared wave function). For a cos(x) wave function, its NBP is simply to lift-up wave function by one to make its min =0, and then divided by two to make its max =1, so its NBP = [1 + cos(x)]/2. The trigonometric formula [1 + cos(x)]/2 = [cos(x/2)}^2 revealed that for a planet doing orbital movement in Solar system, its NBP ground state is n=1, and its Born probability ground state is n = 1/2. We showed that NBP is valid not only for {N,n} QM’s nLL QM state, but also for the 1D infinity deep square potential well QM, for the circular 1D QM, and for the plane wave QM. NBP demonstrates more direct and intuitive physical meaning than that of Born probability. In contrast to that Born probability is only for the standing wave function, NBP is for a uni-directional traveling wave function (which naturally includes the linearly combined two opposite-directional traveling waves, or a standing wave). Therefore, Born probability is possible merely a special case of (the more generalized) NBP. With NBP, we may explain the flute sound wave (an air mass density vibration) mechanics directly as the 1D quantum mechanics! This may significantly change our view on QM and its application on our daily-life-world’s (Newtonian) physics. The planet formation through accretion is also discussed by using NBP.
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[v1] 2020-05-07 13:19:14
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